Monopoly Pricing, Optimal Randomization and Resale

This paper provides a parsimonious and unified explanation for randomized selling mechanisms widely used in practice, yet commonly perceived as puzzling. We show that randomization implemented via opaque pricing and underpricing is optimal only if the revenue function with market clearing pricing is non-concave. Randomization involves conflation and rationing and, relative to market clearing pricing, leads to larger quantities sold. If this quantity effect is sufficiently strong, randomization increases consumer surplus. For fixed quantities resale increases consumer surplus. However, if resale is sufficiently efficient then consumer surplus can be larger under resale prohibition because resale reduces the equilibrium quantities.